If p² + q² - r² = 0, then the value of p⁶ + q⁶ - r⁶ ÷ p²q²r², is:
A man invested \( \frac{1}{2} \) of his capital at 5% rate of interest per annum, \( \frac{1}{3} \) of his capital at 8% per annum and the remaining at 10% rate of interest per annum. His total income from the three investments is ₹820.00 in a year. The total capital invested is:
Select the number from among the given options that can replace the question mark (?) in the following matrix.
| 14 | 12 | 10 | 8 |
| 10 | 8 | 6 | 4 |
| 8 | 6 | 4 | 2 |
| ? | 14 | 12 | 10 |
The length of the longest pole, that could be placed in a room of dimensions 10 m, 8 m and 6 m, is:
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and turned right at Bandra (B) crossing, then at Colaba T-point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route, how much less distance would Sita have actually travelled between the starting point and the destination?